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Reorienting regularn-gons

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Imagine that randomly oriented objects in the shape of a regularn-sided polygon are moving on a conveyor. Our aim is to specify sequences composed of two different rigid motions which, when performed on these objects, will reposition them in all possible ways. We call such sequencesfacing sequences. (Expressed in group theoretical terms, a facing sequence in a groupG is a sequence of elementsa 1,a 2, ...,a n fromG such thatG={e,a 1,a 1 a 2, ...,a 1 a 2 ...a n }). In this paper we classify various kinds of facing sequences and determine some of their properties. The arguments are group theoretical and combinatorial in nature.

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Gallian, J.A., Marttila, C.A. Reorienting regularn-gons. Aeq. Math. 20, 97–103 (1980). https://doi.org/10.1007/BF02190498

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AMS (1970) subject classification

  • Primary 05A15
  • 20F05